Quantile regression for cloud model parameter estimation: a robust approach to uncertainty quantification

As an important tool for characterizing uncertain information, the precision and robustness of cloud model parameter estimation directly affect the reliability of knowledge representation. Existing backward cloud generation algorithms were mostly based on moment estimation or resampling strategies, being sensitive to outliers and unable to fully utilize distributional morphological information in data. This paper proposes a quantile regression-based method, which achieves robust joint estimation of the three numerical features—expected value, entropy, and hyper-entropy—by constructing optimized matching relationships between sample quantiles and theoretical quantiles of cloud models. This method leverages the semiparametric adaptability of quantile regression to distributional morphology and the outlier resistance of median estimation, obtaining consistent parameter estimates without strict distributional assumptions, with median estimation possessing a theoretical breakdown point of fifty percent. Theoretical analysis proves the strong consistency and asymptotic normality of estimators; simulation experiments demonstrate that compared with traditional moment estimation and resampling methods, this algorithm exhibits superior estimation accuracy, algorithmic stability, and comprehensive cloud distance indicators under scenarios including point contamination, scale inflation, and asymmetric tail contamination. This method provides a new statistical perspective and reliable tool for cloud model applications in complex data environments.